Rigging/ Weightpaint problem
It looks like they're just the wrong weights- you would need it to be the same weight as the corresponding area of the neck for it to follow the bones the same way.

What I would recommend is either using the automatic weighting system for the spines if that's how you did the neck, or if the neck's weighting has been manually edited then most likely you would need to use trial and error to manually weight paint the spines on. Anybody else, correct me if I'm wrong, but I don't think there's any way to successfully transfer exact weights to something with such a different shape than the original mesh.